CN110702585A - Rock compression coefficient calculation method - Google Patents
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- 239000011435 rock Substances 0.000 title claims abstract description 176
- 230000006835 compression Effects 0.000 title claims abstract description 60
- 238000007906 compression Methods 0.000 title claims abstract description 60
- 238000004364 calculation method Methods 0.000 title claims abstract description 15
- 239000011148 porous material Substances 0.000 claims abstract description 50
- 230000035699 permeability Effects 0.000 claims abstract description 33
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- 230000002500 effect on skin Effects 0.000 abstract description 7
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- 230000007423 decrease Effects 0.000 description 9
- 230000035945 sensitivity Effects 0.000 description 4
- 238000004458 analytical method Methods 0.000 description 2
- 238000009795 derivation Methods 0.000 description 2
- 239000007789 gas Substances 0.000 description 2
- VNWKTOKETHGBQD-UHFFFAOYSA-N methane Chemical compound C VNWKTOKETHGBQD-UHFFFAOYSA-N 0.000 description 2
- 238000012544 monitoring process Methods 0.000 description 2
- 239000002245 particle Substances 0.000 description 2
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 1
- 238000005056 compaction Methods 0.000 description 1
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Abstract
The invention provides a rock compression coefficient calculation method, which comprises the following steps of measuring the permeability of rocks under different effective overburden pressures and calculating the porosity of a rock sample under the corresponding effective overburden pressure; calculating the pore volume of the rock sample under the corresponding effective overburden pressure; and calculating the compression coefficient of the rock sample under the corresponding effective overburden pressure. According to the method, the rock compression coefficient is calculated according to the measurement results of the rock permeability under different effective overlying pressures, the calculated rock compression coefficient is close to the actually measured rock compression coefficient, the calculation result is reliable, and the problem that the existing actually measured compression coefficient method is influenced by the skin effect can be solved.
Description
Technical Field
The invention belongs to the field of petroleum and natural gas engineering, and particularly relates to a rock compression coefficient calculation method.
Background
The compression coefficient of the rock reflects the elastic energy of the rock, and the accurate determination of the compression coefficient of the rock of the reservoir layer of the oil and gas reservoir is an important prerequisite for accurately evaluating the elastic energy of the oil and gas reservoir.
At present, the method for determining the compression coefficient of the rock comprises a laboratory measurement method, an elastic modulus method, an empirical formula method and a dynamic analysis method. Because a large number of pores exist on the surface of the rock sample, a skin effect can be generated in the process of measuring the rock compression coefficient in a laboratory, so that the measurement result is generally high. The elastic modulus method is a method for calculating the compression coefficient of the rock according to the elastic modulus and the Poisson ratio of the rock, and the method cannot calculate the compression coefficient of the rock under different effective overlying pressures. The empirical formula is an empirical relationship established by a statistical method according to laboratory measured data, and has no general applicability due to a large number of factors influencing the compression coefficient of the rock. The dynamic analysis method is a relational expression established by adopting a substance balance principle according to dynamic monitoring data in the production process, and has strong dependence on the dynamic monitoring data and limited application range.
Disclosure of Invention
The invention provides a calculation method capable of accurately determining rock compression coefficients under different effective overlying pressures according to permeability stress sensitivity experimental data.
The invention provides a rock compression coefficient calculation method, which comprises the following steps,
measuring the permeability of the rock under different effective overburden pressures;
calculating the porosity of the rock sample under the corresponding effective overburden pressure;
calculating the pore volume of the rock sample under the corresponding effective overburden pressure;
and calculating the compression coefficient of the rock sample under the corresponding effective overburden pressure.
Further, in the above-mentioned case,
the calculating the porosity of the rock sample corresponding to the effective overburden pressure includes calculating the porosity using the following formula,
in the formula, k0Is the permeability of the rock sample at an effective overburden pressure of 0 in m2And k is the permeability of the rock sample at different effective overburden pressures in m2；φ0For the porosity of a rock sample at an effective overburden pressure of 0, the numerical value substituted for porosity is a decimal number.
The calculating the pore volume of the rock sample corresponding to the effective overburden pressure comprises calculating the pore volume by adopting the following formula,
in the formula, VpPore volume, m, of rock sample at different effective overburden pressures3；L0The length of the rock sample when the effective overburden pressure is 0 is expressed in m; d0The diameter of the rock sample when the effective overburden pressure is 0 is represented by m, phi is the porosity of the rock sample under different effective overburden pressures, and the numerical value substituted by the porosity is a decimal number.
Further, the air conditioner is provided with a fan,
the calculating the compressibility of the rock sample corresponding to the effective overburden pressure includes,
drawing a relation curve of the pore volume and the effective overlying pressure according to the pore volume of the rock sample under each effective overlying pressure, determining a fitting equation through regression analysis, solving a first derivative of the pore volume under each effective overlying pressure to the effective overlying pressure, substituting the pore volume of the rock sample under different effective overlying pressures and the first derivative of the pore volume to the effective overlying pressure into the following formula, and calculating to obtain the pore volume compression coefficient of the rock sample under each effective overlying pressure,
in the formula, CpThe compression coefficient of the rock is Pa-1(ii) a p is the effective overlying pressure in Pa.
The method has the advantages that the rock compression coefficient is calculated according to the measurement results of the rock permeability under different effective overburden pressures, the calculated rock compression coefficient is close to the actually measured rock compression coefficient, the calculation result is reliable, and the problem that the existing actually measured compression coefficient method is influenced by the skin effect can be solved.
Drawings
FIG. 1 is a graphical representation of permeability versus effective overburden pressure for an embodiment of the present invention.
FIG. 2 is a graph illustrating the relationship between compressibility and effective overlying pressure according to one embodiment of the present invention.
FIG. 3 is a comparison graph of measured values and calculated values of rock sample No. 1 according to an embodiment of the present invention.
FIG. 4 is a comparison graph of measured values and calculated values of rock sample No. 2 according to an embodiment of the present invention.
FIG. 5 is a comparison graph of measured values and calculated values of rock sample No. 3 according to an embodiment of the present invention.
FIG. 6 is a flow chart of the method of the present invention.
Detailed Description
The method is based on permeability stress sensitivity experimental data derivation and establishment of a relational equation of the porosity and the permeability of the rock sample under different effective overburden pressures, the porosity of the rock sample under the corresponding effective overburden pressure is calculated according to the permeability of the rock sample under the different effective overburden pressures, the pore volume of the rock sample under the corresponding effective overburden pressure is further calculated, then the compression coefficient of the rock sample under the corresponding effective overburden pressure is determined according to rock compression coefficient definition, and finally the reliability of the method is verified through example calculation.
A large number of pores exist on the surface of the rock sample, and a skin effect is generated in the process of measuring the compression coefficient of the rock in a laboratory, so that the measurement result is generally high. The invention deduces and establishes a relation equation of rock porosity and permeability under different effective overburden pressures based on a Kozeny-Carman equation, provides a method for calculating the rock compression coefficient based on permeability stress sensitivity experimental data, can solve the problem that the current actual measurement compression coefficient method is influenced by skin effect, and has reliable calculation results.
The derivation and implementation of the method of the present invention will be described with reference to the accompanying drawings.
1 principle of calculation method
1.1 determining the equivalent number of capillaries in a rock sample
When the effective overburden pressure acting on the rock sample is 0, the rock sample has a pore volume of
In the formula: vp0The effective overburden pressure is the pore volume of the rock sample at 0 in m3；VbIs the apparent volume of the rock sample, and the unit is m3；D0The diameter of the rock sample at an effective overburden pressure of 0 is given in m; l is0The length of the rock sample at an effective overburden pressure of 0 is given in m; phi is a0For the porosity of a rock sample at an effective overburden pressure of 0, the numerical value substituted for porosity is a decimal number.
The pores of the rock sample are equivalent to capillaries, and when the effective overlying pressure is 0, the pore volume of the rock sample is
In the formula: n is the number of capillaries in the rock sample; r is0The radius of the capillary at an effective overburden pressure of 0 is given in m; tau is0For effective capillary tortuosity at an overburden pressure of 0, tau0Is a pure number with no physical units.
When the normal pressure permeability of the rock sample is measured, the effective overlying pressure is 2.0MPa, and the effective overlying pressure is smaller and can be approximately regarded as 0. According to the Kozeny-Carman equation, the effective overburden pressure is 0 and the capillary radius of the rock sample is
In the formula: k is a radical of0The permeability of the rock sample at an effective overburden pressure of 0 is given in m2。
Substituting formula (3) for formula (2) to obtain
Combining formula (1) and formula (4), the equivalent number of capillaries that can obtain a rock sample is
1.2 determining the porosity of rock samples at different effective overburden pressures
The rock is a compact medium, the elastic modulus of rock skeleton particles is large, the hardness of the rock skeleton particles is large, the effective overlaying pressure is changed, the deformation of the rock skeleton is small, the change of the volume of the rock skeleton can be ignored, and the skeleton volume of the rock sample under different effective overlaying pressures is
In the formula: vsIs the volume of the rock sample skeleton in m3。
Along with the increase of the effective overlying pressure, the rock is compressed, the radius of the capillary of the rock sample is reduced, and the pore volume of the rock sample is
Vp＝nπr2L0τ0(7)
In the formula: vpIs the pore volume of the rock sample under different effective overburden pressures, and the unit is m3(ii) a r is the radius of the capillary tube in m at different effective overlying pressures.
As the effective overburden pressure increases, the rock is compressed and the permeability of the rock sample decreases. The permeability under different effective overburden pressures is measured, and the capillary radius of the rock sample under each effective overburden pressure is obtained according to the Kozeny-Carman equation
In the formula: k is the permeability of the rock sample at different effective overburden pressures in m2(ii) a Phi is the porosity, pore, of the rock sample at different effective overburden pressuresThe value of the slot substitution is a decimal number.
Substituting formula (5) and formula (8) for formula (7) can obtain the pore volume of rock sample under different effective overburden pressures
According to the definition of porosity, the porosity of the rock sample under different effective overlying pressures is
The formula (6) and the formula (9) are substituted into the formula (10) and are arranged, so that a one-dimensional quadratic equation about the porosity of the rock sample can be obtained
By solving the equation (11), the porosity of the rock sample under different effective overburden pressures can be obtained
If the permeability of the rock sample under different effective overburden pressures is measured, the porosity of the rock sample under each effective overburden pressure can be calculated by adopting the formula (12).
1.3 determining the compression coefficient of rock sample under different effective overburden pressures
According to the volume compressibility of rock pores, is defined as
In the formula: cpIs the compression coefficient of rock in Pa-1(ii) a p is the effective overlying pressure in Pa.
From equation (13), if the pore volume of the rock sample under different effective overburden pressures and the first derivative of the pore volume to the effective overburden pressure are determined, the pore volume compressibility of the rock sample under each effective overburden pressure can be calculated.
And (3) calculating the porosity of the rock sample under each effective overburden pressure by adopting a formula (12) according to the measured permeability of the rock sample under different effective overburden pressures, and calculating the pore volume of the rock sample under each effective overburden pressure by adopting a formula (9).
And drawing a relation curve of the pore volume and the effective overlying pressure according to the pore volume of the rock sample under each effective overlying pressure, determining a fitting equation through regression analysis, and solving a first derivative of the pore volume under each effective overlying pressure to the effective overlying pressure.
The pore volume of the rock sample under different effective overlying pressures and the first derivative of the pore volume to the effective overlying pressure are substituted into the formula (13), and the pore volume compression coefficient of the rock sample under each effective overlying pressure can be calculated.
The effectiveness and accuracy of the invention is illustrated by a specific example below.
In the embodiment of the invention, referring to SY/T5358-2010 reservoir sensitivity flow experiment evaluation method, the permeability of three sandstone rock samples (table 1) under different effective overburden pressures (figure 1) is measured. From fig. 1: permeability decreases with increasing effective overburden pressure; when the effective overlying pressure is relatively small (the effective overlying pressure is less than 15MPa), the permeability is rapidly reduced along with the increase of the effective overlying pressure; when the effective overburden pressure is relatively large (the effective overburden pressure is greater than 15MPa), the permeability slowly decreases as the effective overburden pressure increases.
TABLE 1 core basic parameter Table
The effective overburden pressure increases, the rock is compressed, and the rock pore radius decreases (equivalent capillary radius decreases), resulting in a decrease in rock permeability. When the effective overburden pressure is relatively small, the rock compression degree is relatively low, the rock compressibility is relatively strong, and therefore the rock pore radius is rapidly reduced along with the increase of the effective overburden pressure, and the permeability of a rock sample is rapidly reduced. When the effective overburden pressure is relatively large, the rock compression degree is relatively high, the rock compressibility is relatively weak, and therefore the rock pore radius is slowly reduced along with the increase of the effective overburden pressure, so that the permeability of the rock sample is slowly reduced.
According to the measured permeability of the rock sample under different effective overburden pressures, the method is adopted to calculate and obtain the compression coefficient of the rock sample under each effective overburden pressure (figure 2). From fig. 2 it can be seen that: as the effective overlying pressure is increased, the rock is compressed, the pore radius of the rock is reduced (the radius of an equivalent capillary tube is reduced), so that the compactness of the rock is increased, and the compression coefficient of the rock is reduced along with the increase of the effective overlying pressure; when the effective overlying pressure is relatively small (the effective overlying pressure is less than 15MPa), the compression coefficient is sharply reduced along with the increase of the effective overlying pressure because the compression degree of the rock is relatively low and the compressibility of the rock is relatively strong; at relatively high effective overburden pressures (effective overburden pressures greater than 15MPa), the compressibility of the rock is relatively weak due to the relatively high degree of compression of the rock, and thus the compression factor decreases slowly with increasing effective overburden pressure.
In this example, the compressibility of the rock sample at different effective overburden pressures was determined as shown in FIGS. 3, 4 and 5 with reference to SY/T5815-2016 rock pore volume compressibility determination method. Fig. 3 is a comparison graph of measured values and calculated values of the rock sample No. 1 in this embodiment, fig. 4 is a comparison graph of measured values and calculated values of the rock sample No. 2 in this embodiment, and fig. 5 is a comparison graph of measured values and calculated values of the rock sample No. 3 in this embodiment. From fig. 3, fig. 4, and fig. 5, it is seen that the rock compression coefficient calculated by the method of the present invention is closer to the actually measured compression coefficient, which indicates that the calculation result of the method of the present invention is reliable. From fig. 3, fig. 4 and fig. 5, it can be seen that the actually measured compression coefficients are all higher than the rock compression coefficient calculated by the method of the present invention to a different extent, because a large number of pores exist on the surface of the rock sample, a skin effect is generated in the process of measuring the rock compression coefficient in a laboratory, so that the measurement result is generally higher, which also indicates that the rock compression coefficient calculated by the method of the present invention is closer to the actual compression coefficient of the rock.
3 conclusion
(1) The invention provides a method for measuring the permeability of rocks under different effective overburden pressures, calculating the porosity of the rocks according to a porosity and permeability relation equation deduced and established by the invention, then calculating the pore volume of the rocks, and finally calculating the compression coefficient of the rocks according to the definition of the compression coefficient of the rocks.
(2) As the effective overlying pressure increases, the rock is compressed, the degree of compaction of the rock increases, the compressibility of the rock decreases, and the compression coefficient of the rock correspondingly decreases. Along with the increase of the effective overlying pressure, the rock compactness is increased rapidly and then slowly, and correspondingly, the compression coefficient of the rock is decreased rapidly and then slowly.
(3) The method calculates the rock compression coefficient according to the measurement results of the rock permeability under different effective overburden pressures, the calculated rock compression coefficient is close to the actually measured rock compression coefficient, the calculation result is reliable, and the method can solve the problem that the existing actually measured compression coefficient method is influenced by the skin effect.
Claims (3)
1. A rock compression coefficient calculation method is characterized by comprising the following steps,
the permeability of the rock at different effective overburden pressures was determined.
Calculating the porosity of the rock sample under the corresponding effective overburden pressure;
calculating the pore volume of the rock sample under the corresponding effective overburden pressure;
and calculating the compression coefficient of the rock sample under the corresponding effective overburden pressure.
2. A rock compressibility factor calculation method as claimed in claim 1,
the calculating the porosity of the rock sample corresponding to the effective overburden pressure includes calculating the porosity using the following formula,
in the formula, k0Is the permeability of the rock sample at an effective overburden pressure of 0 in m2K is different fromPermeability of rock sample under effective overburden pressure in m2(ii) a Phi is the porosity of the rock sample under different effective overburden pressures; phi is a0Is the porosity of the rock sample at an effective overburden pressure of 0.
The calculating the pore volume of the rock sample corresponding to the effective overburden pressure comprises calculating the pore volume by adopting the following formula,
in the formula, VpPore volume, m, of rock sample at different effective overburden pressures3；L0The length of the rock sample when the effective overburden pressure is 0 is expressed in m; d0The diameter of the rock sample at an effective overburden pressure of 0 is given in m.
3. The method of claim 2, wherein calculating the compressibility of the rock sample for the effective overburden pressure comprises,
drawing a relation curve of the pore volume and the effective overlying pressure according to the pore volume of the rock sample under each effective overlying pressure, determining a fitting equation through regression analysis, solving a first derivative of the pore volume under each effective overlying pressure to the effective overlying pressure, substituting the pore volume of the rock sample under different effective overlying pressures and the first derivative of the pore volume to the effective overlying pressure into the following formula, and calculating to obtain the pore volume compression coefficient of the rock sample under each effective overlying pressure,
in the formula, CpIs the compression coefficient of rock in Pa-1(ii) a p is the effective overlying pressure in Pa.
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Cited By (5)
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| CN112146983A (en) * | 2020-09-24 | 2020-12-29 | 大连民族大学 | Non-dimensionalized soil compression coefficient representation method |
| CN112525803A (en) * | 2021-02-10 | 2021-03-19 | 西南石油大学 | Sandstone porosity effective stress coefficient calculation method based on clay shell model |
| CN112800632A (en) * | 2021-04-01 | 2021-05-14 | 西南石油大学 | Sandstone reservoir permeability effective stress coefficient calculation method based on granular model |
| CN113536218A (en) * | 2021-07-13 | 2021-10-22 | 中国石油大学(北京) | Method and device for calculating rock pore volume compression coefficient |
| CN113916738A (en) * | 2020-07-07 | 2022-01-11 | 中国石油化工股份有限公司 | Method for measuring pore compression coefficient of crack medium |
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112146983B (en) * | 2020-09-24 | 2023-11-03 | 大连民族大学 | Dimensionless soil body compression coefficient representation method |
| CN112525803A (en) * | 2021-02-10 | 2021-03-19 | 西南石油大学 | Sandstone porosity effective stress coefficient calculation method based on clay shell model |
| CN112800632A (en) * | 2021-04-01 | 2021-05-14 | 西南石油大学 | Sandstone reservoir permeability effective stress coefficient calculation method based on granular model |
| CN113536218A (en) * | 2021-07-13 | 2021-10-22 | 中国石油大学(北京) | Method and device for calculating rock pore volume compression coefficient |
| CN113536218B (en) * | 2021-07-13 | 2023-06-06 | 中国石油大学(北京) | Method and device for calculating rock pore volume compression coefficient |
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